When a sensor array is configured to detect and estimate a signal of interest in an environment that also includes sources of noise and interference, a beamformer may be used to increase the signal-to-noise ratio of the signal of interest, thus improving its detection and estimation. The term “beamformer” refers here to a software program executable by a processor of a computing device, or to an ASIC, FPGA, or other hardware implementation of the logic of such a program, which filters and combines the signals received by a sensor array. The beamformer is designed so that a signal of interest arriving from a prescribed direction is preserved but the noise and interference arriving from other directions are suppressed. For example, a beamformer may be used to isolate the sound of one instrument in an orchestra.
The most common methods for beamformer design rely on statistical models using covariance matrices. Beamformer design assumes knowledge of the covariance matrix of the noise and interference (called Sn below) for each frequency band of interest. This covariance matrix provides a description of the undesired signals impinging on the array, which may be cancelled or suppressed to improve the signal-to-noise ratio of the processed signal.
Algorithms to estimate Sn often include determining when the source of interest is not active (for example, when a speaker is not talking); this determination may then be used to gate the update of Sn. Unfortunately, this gating is imperfect and can have incorrect timing even under moderate signal-to-noise ratio conditions. Furthermore, in some applications the source of interest may be continuously active (for example, a piano during a concert), such that no gating mechanism exists. A beamformer generated under these conditions may have a sample covariance estimate of Sn that includes the signal of interest. Thus, the beamformer may treat the signal of interest as noise and attempt to cancel it. Techniques developed to avoid this signal cancellation effect generally have side-effects, such as loss of optimality of the designed beamformer.